Asymptotics of the system of solutions of a general differential equation with parameter
We consider annth-order differential equation $$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$ with parameter λ ∈ ℂ on a finite interval [a,b]. Under the conditions that \(j = \overline {1,n} \) anda 0 (x) is an absolutely continuous function which does not tu...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5367 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865792580815421440 |
|---|---|
| author | Rykhlov, V. S. Рыхлов, В. С. Рыхлов, В. С. |
| author_facet | Rykhlov, V. S. Рыхлов, В. С. Рыхлов, В. С. |
| author_institution_txt_mv | [
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"author": "В. С. Рыхлов",
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| author_sort | Rykhlov, V. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:31:25Z |
| description | We consider annth-order differential equation $$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$ with parameter λ ∈ ℂ on a finite interval [a,b]. Under the conditions that \(j = \overline {1,n} \) anda 0 (x) is an absolutely continuous function which does not turn into zero on the interval [a, b], we establish asymptotic formulas of exponential type for the fundamental system of solutions of this equation provided that |λ| is sufficiently large. |
| first_indexed | 2026-03-24T03:15:25Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5367 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:15:25Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c2/853b1b41bc3612fde525d909bfcd5dc2.pdf |
| spelling | umjimathkievua-article-53672020-03-18T21:31:25Z Asymptotics of the system of solutions of a general differential equation with parameter Асимптотика системы решений дифференциального уравнения общего вида с параметром Rykhlov, V. S. Рыхлов, В. С. Рыхлов, В. С. We consider annth-order differential equation $$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$ with parameter λ ∈ ℂ on a finite interval [a,b]. Under the conditions that \(j = \overline {1,n} \) anda 0 (x) is an absolutely continuous function which does not turn into zero on the interval [a, b], we establish asymptotic formulas of exponential type for the fundamental system of solutions of this equation provided that |λ| is sufficiently large. Розглянуто диференціальне рівняння $n$-го порядку на скінченному відрізку $[a, b]$ з параметром $λ ∈ ℂ$ вигляду $$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$ При умовах $λ ∈ ℂ,\; [a, b], j = \overline {1,n}, a_0 (x)$ —абсолютно неперервна функція, яка не має нульового значення на $[а, Ь]$, одержані асимптотичні формули експоненціального типу для фундаментальної системи розв'язків цього рівняння при достатньо великих значеннях $|λ|$. Institute of Mathematics, NAS of Ukraine 1996-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5367 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 1 (1996); 96-108 Український математичний журнал; Том 48 № 1 (1996); 96-108 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5367/7425 https://umj.imath.kiev.ua/index.php/umj/article/view/5367/7426 Copyright (c) 1996 Rykhlov V. S. |
| spellingShingle | Rykhlov, V. S. Рыхлов, В. С. Рыхлов, В. С. Asymptotics of the system of solutions of a general differential equation with parameter |
| title | Asymptotics of the system of solutions of a general differential equation with parameter |
| title_alt | Асимптотика системы решений дифференциального уравнения общего вида с параметром |
| title_full | Asymptotics of the system of solutions of a general differential equation with parameter |
| title_fullStr | Asymptotics of the system of solutions of a general differential equation with parameter |
| title_full_unstemmed | Asymptotics of the system of solutions of a general differential equation with parameter |
| title_short | Asymptotics of the system of solutions of a general differential equation with parameter |
| title_sort | asymptotics of the system of solutions of a general differential equation with parameter |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5367 |
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